Shows such as F.R.I.E.N.D.S use a pre-made song for their opener. However, other shows, like New Girl, use a unique song specific for their show. Would you prefer a catchy tune specific to the show or a popular song often heard on the radio for a shows opening?
Depends on the show, if it's a good song then it's much preferred that they make their own intro theme, game of thrones is the perfect example of this, the score was perfect for the tone of the show.
I think I would almost always prefer a song that's unique to the show. I can associate many good theme songs with shows that I like, and they are almost always songs I'd never heard before.